Abstract
We consider two spin-1/2 particles with isotropic Heisenberg interaction, as the working substance of a quantum heat engine. We observe a frictional effect on the adiabatic branches of the heat cycle, which arises due to an inhomogeneous driving at a finite rate of the external magnetic field. The frictional effect is characterized by entropy production in the system and reduction in the work extracted. Corresponding to a sudden and a very slow driving, we find expressions for the lower and upper bounds of work that can be extracted on the adiabatic branches. These bounds are also confirmed with numerical simulations of the corresponding Liouville-von Neumann equation.
Similar content being viewed by others
References
A. Calogeracos, G.E. Volovik, J. Exp. Theor. Phys. Lett. 69, 281 (1999)
R. Kosloff, T. Feldmann, Phys. Rev. E 65, 055102 (2002)
T. Feldmann, R. Kosloff, Phys. Rev. E 68, 016101 (2003)
K. Ahn, P. Mohanty, Phys. Rev. Lett. 90, 85504 (2003)
T. Feldmann, R. Kosloff, Phys. Rev. E 73, 025107 (2006)
Y. Rezek, Entropy 12, 1885 (2010)
R. Kosloff, Entropy 15, 2100 (2013)
E. Geva, R. Kosloff, J. Chem. Phys. 96, 3054 (1992)
M.O. Scully, M.S. Zubairy, G.S. Agarwal, H. Walther, Science 299, 862 (2003)
J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics (Springer, Berlin, 2004)
A. Allahverdyan, T. Nieuwenhuizen, Phys. Rev. E 29, 74 (2005)
A. Allahverdyan, T. Nieuwenhuizen, Phys. Rev. E 71, 46107 (2005)
M.J. Henrich, M. Michel, G. Mahler, Europhys. Lett. 76, 1057 (2006)
A.E. Allahverdyan, R.S. Johal, G. Mahler, Phys. Rev. E 77, 041118 (2008)
N. Linden, S. Popescu, P. Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010)
S. Abe, Phys. Rev. E 83, 041117 (2011)
T. Feldmann, R. Kosloff, Phys. Rev. E 85, 051114 (2012)
G. Thomas, R.S. Johal, Phys. Rev. E 83, 031135 (2011)
X. Hu, R. de Sousa, S. Das Sarma, Phys. Rev. Lett 86, 918 (2001)
D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)
M. Asoudeh, V. Karimipour, Phys. Rev. A 71, 022308 (2005)
E. Albayrak, Eur. Phys. J. B 72, 491 (2009)
T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004)
T.D. Kieu, Eur. Phys. J. D 39, 115 (2006)
T. Zhang, W.-T. Liu, P.-X. Chen, C.-Z. Li, Phys. Rev. A 75, 062102 (2007)
M. Born, V. Fock, Z. Phys. 51, 165 (1928)
T. Kato, J. Phys. Soc. Jpn 5, 435 (1950)
R. Alicki, J. Phys. A 12, L103 (1979)
J. Keeler, Understanding NMR spectroscopy (John Wiley & Sons, New York, 2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Thomas, G., Johal, R.S. Friction due to inhomogeneous driving of coupled spins in a quantum heat engine. Eur. Phys. J. B 87, 166 (2014). https://doi.org/10.1140/epjb/e2014-50231-1
Received:
Published:
DOI: https://doi.org/10.1140/epjb/e2014-50231-1